Irreducible tensor product modules over the affine-Virasoro algebra of type A1

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A(1) by taking the tensor product of irreducible U(h)-free modules of rank 1 with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type A(1), and give sufficient and necessary conditions for these induced modules to be reducible.